The goal of image restoration is to operate on an image signal that has been degraded by noise (such as film grain, scanner, or quantization noise) to remove the noise from the image signal and restore the image signal to its undergraded condition.
In one type of image restoration technique, statistical models of the image process and the noise process are constructed, and operations are performed on the noise degraded image signal to undo the effects of the noise process on the image signal. One such approach is to minimize a function of the error between the original image and the processed image. The operation on the image signal is called a minimum error filter. Minimum error filters can be derived from a priori and/or a posteriori knowledge about the statistics of the image and noise processes. A priori knowledge is that which is known before examining the degraded image signal, and a posteriori knowledge is that which can be determined by examining the noise degraded image signal itself.
A minimum mean-square error filter derived substantially from a priori knowledge is generally referred to as a Wiener filter. The minimum uniform error filter derived from a priori and a posteriori knowledge is generally referred to as a maximum a posteriori (MAP) filter. The MAP filter is a linear filter that maximizes the a posteriori probability for a linear imaging system.
The successful design of a MAP filter requires an estimate of the signal and noise probability density functions (pdf's) of the signal and noise. It has been shown that the MAP filter produces optimum results in the presence of uncertainty about the statistics of the image and noise processes. See H. J. Trussel, "Notes on Linear Image Restoration by Maximizng the A Posteriori Probability," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP 26, No. 2, April 1978.
Unfortunately, the statistics of images vary considerably from image to image (i.e. the image statistics are not stationary) and although the linear MAP filter is more robust than other statistical filters in the presence of uncertainty about image statistics, the usefulness of the MAP filter is still limited due to the large variability in statistics from image to image.
It is an object of the present invention to provide a signal processing method for reducing noise in an image signal incorporating the advantages of a MAP filter that overcomes the shortcomings noted above due to the lack of stationary of the statistics of image signals.
In digital image transmission systems employing differential pulse code modulation DPCM (see DIGITAL IMAGE PROCESSING by William K. Pratt; John Wiley and Sons N.Y.; page 641) the difference between an actual pixel value, and its estimate, produced by a predictor, is quantized and coded for transmission over a communication channel. At a receiver, the decoded difference signal is reconstructed and combined with an estimate from a predictor identical to the one in the transmitter to reconstruct the original image. It is a further object of the present invention to incorporate the advantages of a MAP filter in a DPCM digital image transmission system to remove noise from the transmitted image signal.